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6. Quantum Physics
In a radical departure from classical ideas, theoretical physicist Max Planck proposed that energy
travels in discrete packets called quanta. Prior to Planck’s work with black body radiation, energy
was thought to be continuous, but this theory left many phenomena unexplained. While working
out the mathematics for the radiation phenomena he had observed, Planck realised that quantised
energy could explain the behaviour of light. His revolutionary work laid the foundation for much of
modern physics.
In 1900 Max Planck began to study the range of electromagnetic radiation that emanates from a
very hot body (black body radiation). When a body is heated, it first glows red; with further heating
it turns to white and eventually blue (ie. the wavelength of light emitted becomes shorter and it
frequency becomes higher with increasing temperature).
Experiments showed that the amount of energy that is emitted falls off to zero at high and low
wavelengths. As the temperature of the body changes, the hump in the energy distribution curve
shift.
Planck attempted to use classical theory to explain the strange behaviour of this distribution curve.
Classical theory predicted that the amount of energy emitted by a hot body should increase
continuously as the frequency increases. Planck could not explain the observed energy
distribution using classical theory, so he developed a new concept. This was that energy is
radiated in discrete packets or bundles called quanta (singular: a quantum), rather than in
continuous amounts as Wave Theory implies. The energy-radiated (E) is proportional to the
frequency (f) of the radiation. The two quantities were connected by a proportionality constant (h).
E=
hc

c = speed of light.
This is also written as E = hf where f is the frequency of the light.
Photons
The modern theory of light is a merging of the wave and the particle models. Light is imagined to
travel in a stream of packets or quanta of energy. The energy carried by each quantum is
proportional to the frequency of light and can be found from Planck’s equation: E = hf. Greater
intensity of light has more photons - each photon still has the same energy.
Photons are neither particles nor waves. They have a set of properties that have some similarities
to particles when travelling through a vacuum and when in a gravity field, and some similarities to
waves when refracting and interfering.
Wave-Particle duality of light
The paradoxical view of the nature of light was built into Einstein’s original formulation of the
photon model. The energy of the light was supposed to be carried in the form of a particle or
photon, the energy of the photon was defined in terms of the frequency of the radiation, and
frequency is an essentially wavelike property! One possible way of dealing with this paradox is to
treat light as a wave some of the time and as a particle at other times.
The behaviour of waves varies across the electromagnetic spectrum. Low frequency photons
such as radio-waves and microwaves exhibit distinctly wave-like behaviours such as diffraction
and interference, but have no particle-like properties. Around the middle of the spectrum in the
visible light region, photons have both wave and particle properties. They interfere and diffract like
waves, and also interact with electrons in the photoelectric effect as particles do. At the high
frequency end of the spectrum, X-ray and gamma ray photons behave much more like particles
than waves.
The momentum of Photons
Quantum mechanics is the fundamental theory of small scale phenomena, such as the properties
of electrons, photons and atomic interactions. Classical physics deals with continuous quantities,
whereas quantum mechanics shows that on the very small scale, all quantities are discrete or
quantised. In particular, at the quantum level, the distinction between wave and particle becomes
blurred. The mathematics of quantum theory tends to produce probabilities rather than inviolate
numbers indicating an inherent randomness in small-scale phenomena.
In 1923, Compton showed that X-ray photons could collide with electrons and scatter, leaving with
a longer wavelength (less energy) than before. This is only possible if the photons were able to
transfer momentum and hence energy to the electrons.
Before collision
photon
Electron at rest

After collision
v

Maxwell suggested that photons do have momentum given by
p=
E
c
where c is the speed of light and E is the energy of the photon.
As the energy of the photon is related to its frequency by Planck’s equation, and, since
c = f for waves, the momentum equation can be written as
p=
hf
h
=

c
De Bröglie argued that the universe should be symmetrical and that the equation p=h/ should
apply to particles as well as waves. A particle’s momentum is given by p = mv and so
p = mv =
h

=
h
mv
The wavelength calculated is called the De Bröglie wavelength for the particle
When sound and light waves pass through narrow slits, they show diffraction effects only when the
slit is about 1-50 . Thus, a particle could be expected to show diffraction only if it is passing
through a gap 1-50 times its De Bröglie wavelength. For most large particles this is impractical as
the physical size of the particle is far too large.
Only in the case of small particles such as electrons, is the De Bröglie wavelength enough for
diffraction and interference effects to occur.
Properties of photons with similarities to waves and or particles
Speed depends on the medium
Two light beams can pass through each other without interacting.
When light passes from one medium to another, refraction occurs.
Light diffracts when travelling through narrow openings
Different colours correspond to different energies of light.
Reflection from a shiny surface occurs such that the angles of
incidence and reflection are the same.
Light exerts a pressure
Travels through a vacuum as well as transparent media.
Beams of light are bent (a little) by gravity.
Certain colours (energies) of light can cause electrons to be ejected
from metal surfaces.
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